Question

Find the number of terms, n, in the arithmetic series whose first term is 15, the common difference is 4, and the sum is 3219. Pls I need help ASAP I will give top answer.

A. 33
B. 35
C. 37
D. 36

Answer 1

To determine the number of terms in the arithmetic series, we use the sum formula for arithmetic series and solve the resulting quadratic equation. Upon solving, we find that the series has 37 (C) terms.

Step-by-step explanation:

To find the number of terms, n, in the arithmetic series with the first term a as 15, the common difference d of 4, and the sum S of the series as 3219, we can use the formula for the sum of an arithmetic series:

• S = n/2 * (2a + (n - 1)d)

Plugging in the values given:

• 3219 = n/2 * (2*15 + (n - 1)*4)

Now, we simplify and solve for n:

• 3219 = n/2 * (30 + 4n - 4)

• 3219 = n/2 * (4n + 26)

• 6438 = n(4n + 26)

We now have a quadratic equation:

• 4n² + 26n - 6438 = 0

Divide all terms by 2 to simplify:

• 2n² + 13n - 3219 = 0

Factorizing the equation

• 2n²+ 87n-74n- 3219=0
• n(2n+87) - 37(2n+87)=0
• n= 37, n= -(87/2)

We can solve this equation using the quadratic formula or by factoring if possible. Upon solving, we find that n = 37 is a valid positive integer solution that satisfies the equation.

Therefore, the arithmetic series has 37 terms.

Answer 2

Answer: 37

Step-by-step explanation:

I guessed on the quiz and got it right